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Choose parts, repeat it, or solve the returning integral

Integrate with respect to xx: (a) (2x+3)ln⁡x(2x+3)\ln x; (b) xsin⁡xx\sin x; (c) ln⁡x\ln x; (d) x2cos⁡xx^2\cos x; (e) e2xsin⁡xe^{2x}\sin x.

CJC · Lecture · Example 17

LIATE is a guide for selecting u, not an absolute rule; the Teacher explicitly notes exceptions.

The source stresses repeated parts and collecting a returning integral rather than continuing indefinitely.

Read the worked solution